Nowhere-zero $3$-flow and ${\mathbb{Z}}_3$-connectedness in Graphs with Four Edge-disjoint Spanning Trees

Miaomiao Han, Hong-Jian Lai, Jiaao Li

Given a zero-sum function $\beta :V(G)\to {\mathbb{Z}}_3$ with ${\sum }_{v\in V(G)}\beta (v)=0$, an orientation $D$ of $G$ with $d_D^{+}(v)-d_D^{-}(v)=\beta (v)$ in ${\mathbb{Z}}_3$ for every ver…